Robust analogs to the coefficient of variation

Abstract

The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect it. Additionally, for skewed distributions the mean and standard deviation may be difficult to interpret and, consequently, that may also be the case for the $\mathrm{CV}$. Here we investigate the extent to which quantile-based measures of relative dispersion can provide appropriate summary information as an alternative to the CV. In particular, we investigate two measures, the first being the interquartile range (in lieu of the standard deviation), divided by the median (in lieu of the mean), and the second being the median absolute deviation, divided by the median, as robust estimators of relative dispersion. In addition to comparing the influence functions of the competing estimators and their asymptotic biases and variances, we compare interval estimators using simulation studies to assess coverage.

Keywords:

• Influence function
• median absolute deviation
• quantile density

2010 Mathematics Subject Classification:

• 62G35

Acknowledgments

The authors are very thankful to the referee, Associate Editor and Editor for their suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).